Databricks·Software Engineer·Technical Phone Screen·Intermediate

Intermediate

Jun 2026

Summary

Databricks SWE interview with a graph/grid traversal problem that had a twist I didn't see coming. The multi-modal cost-vs-time tiebreaker made it more interesting than a plain shortest path question.

Questions Asked (1)

Given a city grid with multiple transportation modes, each having their own cost and time matrices, find the fastest route from a source cell to a destination. If two modes arrive at the same time, pick the cheaper one.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

My first instinct was modified Dijkstra and that was right, but I fumbled the tiebreaker logic for a bit.

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AI HintsAI Generated

Suggested Approach

Model the problem as a shortest path on a state graph where each state is (cell, mode), and edges represent moving to adjacent cells using the same mode or switching modes at the current cell. Use Dijkstra's algorithm with a priority queue ordered by (time, cost) to find the optimal path, ensuring that when times are equal, the lower cost is preferred. Finally, reconstruct the path and return the sequence of cells and modes.

Pro tip: Clarify upfront whether mode switching is allowed only at certain cells (e.g., transfer stations) or anywhere; this assumption drastically changes the graph and algorithm. Also, discuss how to handle large grids by using early termination and bidirectional search if applicable.

1. Clarify assumptions and constraints

Ask about grid size, number of modes, whether switching modes is allowed anywhere or only at specific cells, and if costs/times are static. Confirm the tie-breaking rule: minimize time first, then cost.

2. Define the state space and graph

Create a state for each (cell, mode) pair. Add edges for moving to adjacent cells with the same mode (using that mode's time and cost) and for switching modes at the same cell (with zero time and cost, unless specified otherwise).

3. Choose and justify the algorithm

Use Dijkstra's algorithm because edge weights (time) are non-negative. Maintain a priority queue keyed by (time, cost) to handle the tie-breaking. Mention that A* with a heuristic could be used if performance is critical.

4. Handle tie-breaking and path reconstruction

When relaxing edges, if a new path has equal time but lower cost, update the state. Keep parent pointers to reconstruct the optimal path, including mode switches.

5. Analyze complexity and discuss optimizations

State that the time complexity is O((V+E) log V) where V = cells × modes and E is the number of transitions. Discuss potential optimizations like early termination when the destination is reached, bidirectional search, or using a heuristic.

Key Points to Mention

State space expansion: each cell and mode combination is a node.
Dijkstra's algorithm with a priority queue ordered by (time, cost).
Tie-breaking rule: when times are equal, prefer the path with lower cost.
Mode switching edges: zero-cost and zero-time transitions at the same cell (if allowed).
Path reconstruction using parent pointers to output the sequence of moves.
Complexity analysis and potential optimizations for large grids.

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.